In this paper we will present a formulation for solving elastodynamic problems in 2D using the method of fundamental solutions (MFS). The governing equation for the displacement in the elastodynamic problem is expressed by the Navier equation with an additional non-homogeneous inertial term, which involves the second derivative of displacement with respect to time. The inertial term is approximated by the Houbolt finite difference formula. In each time step, the solution for the displacement is separated into a homogeneous solution and a particular solution. The homogeneous solution is constructed in terms of the fundamental solutions of the elastostatic problem. The particular solution corresponds to the non-homogeneous inertial term, which is obtained by approximating the inertial term with radial basis functions (RBFs). In addition, a formulation based on the MFS for free vibration analysis of 2D bodies is presented in this paper. By solving several numerical examples, we have demonstrated that the proposed methods are robust and accurate. The convergence of the results with respect to the number of collocation points, the number of internal points, the value of the RBF parameter, and the time step size is also studied.

在本文中，我们将提出一种使用基本解法（MFS）解决二维弹性力学问题的公式。弹性动力学问题中位移的控制方程由Navier方程表示，带有一个附加的非均质惯性项，该项涉及位移相对于时间的二阶导数。惯性项由Houbolt有限差分公式近似。在每个时间步骤中，用于置换的溶液均分为均质溶液和特定溶液。均质解是根据弹性静力学问题的基本解构造的。特定解对应于非均质惯性项，该非均质惯性项是通过用径向基函数（RBF）近似惯性项而获得的。此外，本文提出了一种基于MFS的2D物体自由振动分析的公式。通过解决几个数值示例，我们证明了所提出的方法是可靠且准确的。还研究了关于并置点数，内部点数，RBF参数的值和时间步长的结果的收敛性。